We introduce in this paper the notion of the chromatic number of an oriented graph G (that is of an antisymmetric directed graph) defined as the minimum order of an oriented graph H such that G admits a homomorphism to H. We study the chromatic number of oriented k-trees and of oriented graphs with
The Simple Chromatic Number of Oriented Graphs
β Scribed by Petra Smolikovaa
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 202 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1571-0653
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π SIMILAR VOLUMES
## Abstract Given a simple plane graph __G__, an edgeβface __k__βcoloring of __G__ is a function Ο : __E__(__G__) βͺ __F__(G)βββ {1,β¦,__k__} such that, for any two adjacent or incident elements __a__, __b__ β __E__(__G__) βͺ __F__(__G__), Ο(__a__)ββ βΟ(__b__). Let Ο~e~(__G__), Ο~ef~(__G__), and Ξ(__G_
The oriented chromatic number Ο o ( G) of an oriented graph G = (V, A) is the minimum number of vertices in an oriented graph H for which there exists a homomorphism of G to H. The oriented chromatic number Ο o (G) of an undirected graph G is the maximum of the oriented chromatic numbers of all the
## Abstract A homomorphism from an oriented graph __G__ to an oriented graph __H__ is a mapping $\varphi$ from the set of vertices of __G__ to the set of vertices of __H__ such that $\buildrel {\longrightarrow}\over {\varphi (u) \varphi (v)}$ is an arc in __H__ whenever $\buildrel {\longrightarrow}
We prove that there exist oriented planar graphs with oriented chromatic number at least 16. Using a result of Raspaud and Sopena [Inform. Process. Lett. 51 (